If you are standing on Earth's surface and looking straight up into space, you would not be able to see Earth's curve directly. This is because the Earth's curvature is relatively gradual, and at human scales, it appears flat. The curvature becomes noticeable over large distances, such as when looking at the horizon from a higher vantage point.
When you look up into the sky, your field of view is limited to a relatively small portion of the Earth's surface, and the atmosphere above you appears to extend indefinitely. The atmosphere is relatively thin compared to the Earth's size, so it does not provide a visible curve when looking straight up.
However, if you were to observe the horizon from a higher altitude, such as from an airplane or from space, you would start to notice the Earth's curvature. The higher you go, the more pronounced the curve becomes, allowing you to see a more significant portion of the Earth's spherical shape.
In summary, while standing on Earth's surface and looking straight up into space, the curvature of the Earth is not directly visible due to the relatively small field of view and the atmosphere above you. The Earth's curvature becomes more apparent when observing the horizon from higher vantage points.